2. Methods for estimation tailored to high dimensional inference in cluster-based graphical models.
We develop a new estimation strategy tailored to our final goal, that of constructing approximately Gaussian estimators for the entries of the precision matrices \(^*\)  and \(^*\)  given in (REF ) and (REF ) above. Although we work under the assumption that the data is Gaussian,
likelihood based estimators may be unsatisfactory, as their analysis may require stringent assumptions, as explained above, or may become analytically intractable, as argued in Section REF , for the latent graph. We do propose a method that mimics very closely the principles underlying the construction of an efficient score function for estimation in the presence of high dimensional nuisance parameters, see for instance [1]}, but we do not base it on the corresponding likelihood-derived quantities. We explain the underlying principles in Section REF .
